We modify the expected improvement (EI) acquisition function [1]} of BO to filter out the policies in the repertoire that are potentially unsafe to execute on the robot. More concretely, we define a new acquisition function called Expected Safe Improvement (ESI) as follows:
\(& ESI(\mathbf {x}) = EI(\mathbf {x})\times {1}_{\lambda }(\mathbf {x}) \\& \text{where, } \nonumber \\& {1}_{\lambda }(x) = {\left\lbrace \begin{array}{ll}0 &\quad \text{if } LCB_{c}(\mathbf {x}) < \lambda \\1 &\quad \text{otherwise } \\\end{array}\right.}\) 
